Bound surface limits to a function

Bound surface limits to a function



Consider the following plot of two surfaces


Plot3D[Sin[x y], x^3 + y, x, -1, 1, y, -1, 1, PlotRange -> x, -1, 1, y, -1, 1, z, -1, 1, Mesh -> None]



plot



How can I produce a plot where I limit the the surface plot of $sin(x y)$, to be shown only when its values are above $x^3+y$, or any other given function.




2 Answers
2


Plot3D[ConditionalExpression[Sin[x y], Sin[x y] > x^3 + y],
x, -1, 1, y, -1, 1, PlotRange -> -1, 1, -1, 1, -1, 1, Mesh -> None]



enter image description here



To show both functions


Plot3D[ConditionalExpression[Sin[x y], Sin[x y] > x^3 + y], x^3 + y ,
x, -1, 1, y, -1, 1, PlotRange -> -1, 1, -1, 1, -1, 1,
Mesh -> None, BaseStyle -> Opacity[.7]]



enter image description here


Plot3D[Sin[x y], x, -1, 1, y, -1, 1,
 PlotRange -> -1, 1, -1, 1, -1, 1,
MeshFunctions -> Sin[# #2] - #^3 - #2 &, Mesh -> 0,
MeshShading -> None, Automatic, BoundaryStyle -> None]



enter image description here



You can utilize the option RegionFunction for that:


RegionFunction


Plot3D[Sin[x y], x^3 + y, x, -1, 1, y, -1, 1,
Mesh -> None,
RegionFunction -> (x, y, z [Function] Sin[x y] > (x^3 + y))
]



enter image description here





Equivalently: reg = BoundaryDiscretizeRegion[ImplicitRegion[Sin[x y] > (x^3 + y), x, -1, 1, y, -1, 1]]; Plot3D[Sin[x y], x, y ∈ reg]
– J. M. is computer-less♦
Oct 6 at 9:59


reg = BoundaryDiscretizeRegion[ImplicitRegion[Sin[x y] > (x^3 + y), x, -1, 1, y, -1, 1]]; Plot3D[Sin[x y], x, y ∈ reg]



Required, but never shown



Required, but never shown






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